Monday, September 15, 2014

Why is the Quantity Theory of Money Wrong and can Anything be Salvaged from it?

The quantity theory of money states that when the money supply expands or contracts, this is the cause – when other variables are constant – of proportional or equal changes in the price level.

In the quantity theory, the direction of causation therefore runs from the money supply to the price level, the money supply is assumed to be exogenous, and the money supply function independent in the sense described by Colin Rogers (1989: 244–245).

The standard form of the Cambridge Cash Balance Equation as used today is usually given as follows:

M = kPY orM = kdPY
where M = the quantity of money;k or kd = the amount of money held as cash or money balances;P = the general price level;Y = real value of the volume of all transactions entering into the value of national income (that is, goods and services).

In the Cambridge approach, the variable k was held to be superior to Irving Fisher’s “velocity of circulation” concept V, because, unlike V, k is supposed to be empirically measurable.

Therefore M and P are causally related, if kd and Y are constant (Thirlwall 1999).

I will use the Cambridge Cash Balance Equation in what follows.

Post Keynesians say that the quantity theory is not true for modern advanced capitalist economies, where money is largely endogenous.

Perhaps it might be true for an economy with pure commodity money and an exogenous supply, as Colin Rogers (1989: 175, 244) argues, but even here the idea that the relationship between money supply and price level, even if kd and Y are constant, must necessarily and always be proportional in a real world economy, as compared with an analytic mathematical equation true merely by definition, seems questionable.

Of course, advocates of the quantity theory will appeal to the econometric evidence. Doesn’t this prove their case? Not really. A review of the econometric evidence, as, for example, in a good study like Grauwe and Polan (2005) shows that it is a mixed bag, at best. Some studies show a proportional relationship (e.g., Vogel 1974), but others do not, but merely demonstrate a strong positive correlation (Grauwe and Polan 2005; McCandless and Weber 1995; Dwyer and Hafer 1988). Supporters of the quantity theory respond by saying that, if the data does not show a proportional relationship, then by definition kd and Y must have changed. The trouble is that this starts to render the quantity theory a tautology – the sort of mathematical or analytic a priori statement immune from empirical verification or falsification, because it is not in fact an empirical statement at all.

In reality, there are deeper empirical criticisms of the quantity theory than the mixed evidence on proportionality, because the quantity theory requires certain prior assumptions for the theory to work.

But, before we get to these criticisms, what can be salvaged from the quantity theory?

It is true that the quantity theory captures some basic truths. These are as follows:

(2) so in view of (1), it is not at all surprising that the econometric literature often finds a strong or very strong positive correlation between the money supply changes and price level changes (Grauwe and Polan 2005; McCandless and Weber 1995; Dwyer and Hafer 1988).

(3) it is also true that deflations are often correlated with a falling money supply or decelerations in money supply growth.

To be clear, the issue is not whether an expanding money supply is necessary for a sustained, long-run price inflation. An expanding money supply is indeed a necessary, but not sufficient, condition for price inflation.

But when quantity theorists say that “inflation is always and everywhere a monetary phenomenon” (Friedman 1968: 98) they mean something more than just the basic ideas expressed above.

The crucial issues as raised by the quantity theory as part of its assumptions are:

(1) is the money supply exogenously determined, and is there an independent money supply function?

(2) is the assumption of long-run money neutrality as required for the quantity theory to work a realistic one? (It is true that some naïve versions of the quantity theory would assume even a short-run neutrality, but most modern neoclassical economists are realistic enough to recognise the strong degree of nominal price and wage rigidity that exists in modern economies, which, they admit, causes short-run money non-neutrality.)

(3) is the direction of causation as assumed in the quantity theory equation from left to right (that is, from the money supply to the price level)? That is to say, it is really an exogenously-determined money supply that is the fundamental cause, or driver, of price level changes?

A crucial issue is (1) above: is there an exogenous, independent money supply? Is it the primary, causal origin of changes in the price level?

Quantity theorists are asserting that a truly independent and exogenous money supply is the causal driver of inflation and deflation.

What this means is that normally broad money creation is credit-driven. That is, most money is created by private banks and its quantity is determined by the private demand for it. This is the essence of endogenous money. In an endogenous money system, even the “monetary base” is normally endogenous too, given that the central bank must accommodate the banks’ demand for high-powered money to avoid financial crises and banking panics.

So what of question (1) above?

Post Keynesians contend that a truly independent money supply function does not actually exist in an endogenous money world, because credit money comes into existence because it has been demanded (Rogers 1989: 244–245). So the broad money supply is not independent of money demand, but can be demand-led (Ingham 2004: 53).

Next, what of question (2)?

There is considerable evidence that money can never be neutral, not even in the long run. The concept of neutral money holds that changes in the money supply will only affect nominal values (e.g., money prices, nominal money wages, etc.), not real variables (such as production, employment, and investment). Nevertheless, neoclassical economists accept the evidence that price and wage rigidity is a strong characteristic of the real world. They must then assume that prices and wages are sufficiently flexible in the long run, and that they really do adjust in the long period. The trouble is that there is little evidence for this. Most prices are mark-up prices and relatively inflexible with respect to demand changes in both the short and long run. Most capitalist economies are far from full use of resources, and even in booms businesses make use of stocks and capacity utilisation to manage demand changes, rather than changes in prices.

The mysterious long-run flexibility does not seem to be visible in the data, and the long run is just a sequence of short-run periods anyway.

A further complication in that nominal variables can also be found in contracts, such as debts, production orders, or forward contracts, but these are precisely the things that will not necessarily change when the money supply changes.

And, even if you assume an exogenous money supply, a direction of causation from left to right, and reasonably flexible prices, there will still be Cantillon effects, the phenomenon that price level changes caused by increases in the quantity of money depend on the way new money is injected into the economy, and actually where it affects prices first. That is to say, although prices rise as the exogenous quantity of money increases, contrary to the quantity theory of money, we should not expect prices to rise proportionally, but in a complex manner that depends on who received the money and how they spent it (this idea, as it happens, is used by Austrians as the basis of their own criticism of the quantity theory.)

Finally, what of question (3), concerning the direction of causation?

Under an endogenous money system, the direction of causation is generally from credit demand (via business loans to finance labour and other factor inputs) to money supply increases (Robinson 1970; Davidson and Weintraub 1973).

Therefore the direction of causation generally runs:

(1) business demand for credit (to pay for goods and labour factor inputs, whose prices may have risen against previous production periods) + demand for demand deposits

→ (2) increases in broad money

→ (3) banks’ demand for more reserves (high-powered money) when they need to clear obligations.

→ (4) the central bank creates the needed reserves.

Changes in the general price level are a highly complex result of many factors, and not some simple function of money supply.

This crucial point about the direction of causation in the relationship between money supply and output/prices is discussed by Joan Robinson:

“The correlations to be explained [sc. in the relationship between money supply and real output] could be set out in quantity theory terms if the equation were read right-handed. Thus we might suggest that a marked rise in the level of activity is likely to be preceded by an increase in the supply of money (if M is widely defined) or in the velocity of circulation (if M is narrowly defined) because a rise in the wage bill and in borrowing for working capital is likely to precede an increase in the value of output appearing in the statistics. Or that a fall in activity sharp enough to cause losses deprives the banks of credit-worthy borrowers and brings a contraction in their position. But the tradition of Chicago consists in reading the equation from left to right. Then the observed relations are interpreted without any hypothesis at all except post hoc ergo propter hoc.” (Robinson 1970: 510–511).

So what we can say is that – in contrast to the quantity theory – money supply changes are often the effect of changes in credit demand, production and economic activity, and not the cause of the latter phenomena.

In short, money is generally the effect, not the cause.

Finally, what drives an inflation can be complex, and there is no simple, monocausal explanation. Often inflations are a cost-push phenomenon, in which

(2) prices of other factor inputs rise, and then businesses will need to obtain higher levels of credit from banks.

So inflation might be driven by demand for higher wages or supply-side factors. Hence broad money supply growth rates rise in an endogenous money world which generally accommodates the demand for credit, but this rise precedes further price increases because businesses will generally raise mark-up prices to maintain profit margins at a later time, given that most firms engage in time-dependent reviews and changes of their prices at regular intervals. In extreme situations, a wage–price spiral might break out: this involves the same process as above but in a vicious circle.

"In the Cambridge approach, the variable k was held to be equivalent, but superior, to Irving Fisher’s “velocity of circulation” concept V..."

It's not equivalent. It is the obverse of it. 1/k=V. When you turn a number into a fraction like that you get the opposite. In relation to one a half is the opposite of two and so on.

"the idea that the relationship between money supply and price level must necessarily and always be proportional, even if kd and Y are constant, seems questionable."

If kd and Y are constant the the relationship between M and P is an identity. It is true by definition.

"A review of the econometric evidence, as, for example, in a good study like Grauwe and Polan (2005) shows that it is a mixed bag, at best. Some studies show a proportional relationship (e.g., Vogel 1974), but others do not, but merely demonstrate a strong positive correlation (Grauwe and Polan 2005; McCandless and Weber 1995; Dwyer and Hafer 1988)."

Correlation, even if they found it everywhere, does not prove causation. Endogenous money theorists would say that the rise in the money supply is a passive response to something else (wage inflation, exchange rate depreciation, very high levels of government expenditure in wartime etc).

Just a few comments which I'll throw here as I think it relates to the Cantillon effect issue.

I've always understood the equation of exchange to be an identity of sorts.

MV = GPD or M kd=GPD

The left side of the equation is implicitly defining V or kd.

GDP = PY

The right side is a definition of GDP.

But there is a problem here with how this part of the equation is either stated or reasoned from. The right side is the sum of all transactions (end consumer or value added transactions). So technically it looks like this:

GDP = p1 * y1 + p2 * y2 + . . . + pn * yn

So P and Y are technically vectors and you're taking the dot product of the two. Half of the problem with the quantity theory of money (not the equation of exchange) stems from fallacious reasoning that implicitly assumes P and Y are scalars.

The end result is that the entire equation is an identity (GDP = GDP) though at this point there is no implied causality.

1) You mentioned that kd is empirically measurable? Do mean that in some way independent of the above? I know that's how the FRED measures money velocity depending upon which measure of money used (M1, M2 and MZM) by just taking nominal GDP and dividing it by the money supply under consideration.

2) If Y and kd are held constant, does that mean that an increase in M implies there is an increase in P? (without implying any causality yet).

If P and Y were scalars this would be trivially true. But P and Y are not scalars; they are vectors.

As a result, I think this is ambiguous. What does it mean for Y to remain the same? Does the same quantity of each individual good need to be sold? Because if they aren't, how do you add up, say, 100 lbs of beef and 20 gallons of milk?

And what does it mean for P to increase? How do you add up the incommensurable units?

How do we represent a vector by a scalar?

One approach is to take the norm of the vector. But that doesn't address the incommensurable units. For the prices, they are prices per unit of quantity (say, $/tonnes of iron and $/lbs of bananas.) You can take the norm but without any procedure for adding incommensurable units. . .

4) Regarding the Cantillon effects. . .

This will largely depend on how you represent P as a scalar. Obviously the standard approach is to take a weighted basket of prices. I'm not convinced there's a "correct" or "true" way to do so (perhaps more or less "useful" ways to do so.)

I'm not sure what a Cantillon neutral index would look like or if it's even possible but as Phillip suggested, it probably wouldn't be terribly useful.

5) I think the endogenous question is a fair point on which direction the causality goes.

Although perhaps it's sort of a chicken and the egg thing. If I borrow money to finance an investment, does the newly created money (M) cause the investment (Y) or did my desire to invest (Y) cause me to get the loan (M).

Perhaps it does not matter. *shrug*

6) The other thing that bothers me in all of this is where V / kd fits. I mean these are sort of dummy variables that the quantity theorists hold constant (or make a conditional statement that they are constant.)

For example one cause attributed to hyperinflation is an increase in velocity (perhaps rationalized as "currency rejection" or something like it.)

It IS VERY, VERY, VERY LIKELY to need this. But there is no absolute necessary logical reason.

"(2) so in view of (1), it is not at all surprising that the econometric literature often finds a strong or very strong positive correlation between the money supply changes and price level changes (Grauwe and Polan 2005; McCandless and Weber 1995; Dwyer and Hafer 1988)."

Problematic given my previous point about correlation and causation.

"(3) it is also true that a falling money supply is usually correlated with price deflation."

I doubt this is true. I would imagine that deflations are correlated with DECELERATIONS in the money supply. I just pulled a quick example off FRED:

http://bit.ly/1qRlbm7

Why would the money supply SHRINK in a deflation? Money balances just sit idle. They don't start to disappear. Probably just wouldn't grow as fast.

"An expanding money supply is a necessary, but not sufficient, condition for price inflation."

Again, while in practice it is likely to be necessary I don't see any reason for this in theory.

Here is the essence of endo money: the quantity equation is simply an identity and gives us no CAUSAL explanation of inflation. For that we require an entirely different approach.

"(3) is the direction of causation as assumed in the quantity theory equation from left to right (that is, from the money supply to the price level)?"

THIS IS THE REAL KEY TO THE WHOLE THING. THE WHOLE POST SHOULD REALLY BE REWRITTEN EMPHASISING THIS POINT. EVERYTHING ELSE IS SECONDARY.

"What this means that normally broad money creation is credit-driven. That is, most money is created by private banks and its quantity is determined by the private demand for it. This is the essence of endogenous money. In an endogenous money system, even the “monetary base” is normally endogenous too, given that the central bank must accommodate the banks’ demand for high-powered money to avoid financial crises and banking panics."

All true. I would just add: the CAUSES of inflations is heterogenous (VERY important). There is no Ultimate Theory of inflation. (Although most inflations are driven by wage-price spirals).

"Most capitalist economies are far from full use of resources, and even in booms businesses make use of stocks and capacity utilisation to manage demand changes, rather than changes in prices."

This is the most important paragraph in this sentence. Also: there is no long-run tendency to full employment for any number of reasons.

"Finally, what of question (3), or the direction of causation?"

Again, clearly the most important point. Robinson ultimately said (in that paper maybe?) that the quantity equation was a completely useless identity. It is definitionally true. But it can tell us NOTHING about ANYTHING. In order to do this you must fixed certain variables. But these are not fixed. Ergo: you cannot use it as a theory. End of story.

(2) prices of other factor inputs rise, then businesses will need to obtain higher levels of credit from banks.

So inflation might be driven by demand for higher wages or supply-side factors. Hence broad money supply growth rates rise in an endogenous money world which generally accommodates the demand for credit, but this rise can precede further price increases because businesses will generally raise mark-up prices to maintain profit margins at a later time, given that most firms engage in time-dependent reviews and changes of their prices at regular intervals. In extreme situations, a wage–price spiral might break out: this involves the same process as above but in a vicious circle."

I totally agree with Philip Pilkington that the direction of causation is the key.

In fact, I don't think there is a separate question of endogeneity. In the real world, everything is endogenous (except the past). Whether we treat things as exogenous or endogenous is just about models. The QTM is a one equation model, that has M as the exogenous variable and P as the endogenous variable. But I think most monetarists would agree that M is itself caused by other things and that in a bigger model, M will be endogenous. There is no inconsistency between believing that M is determined by, inter alia, bank lending and believing in the QTM.

Also, I think that most monetarists today do not believe that V or k are constant, but rather that they are independent of changes in the money supply. Perhaps more plausible, but still wrong IMO.

Re "can anything be salvaged" how about this - Musgrave's hastily thought up 5 rules of money and inflation:

1. Nominal GDP varies with the amount of exogenous money (base money) all else equal. If the amount of exo money is excessive, excess inflation occurs.

2. If the amount of exo money held by the private sector is enough, there’d be no need for endogenous money. However endo money tends to drive exo money to near extinction for reasons set out by George Selgin. (See 5th para of his Capitalism Magazine article, “Is Fractional-Reserve Banking Inflationary?”)

3. The amount of exo money can be measured very accurately: it’s simply the total of bank reserves at the central bank, plus the amount that has been issued to the public in the form of notes and coin (though an indeterminant propotion of that gets lost or destroyed) thus the amount of exo money cannot be measured with COMPLETE accuracy.

4. The amount of endo money is VERY indeterminant because there is no sharp dividing line between current accounts at commercial banks (which is clearly money) and deposit accounts where access to the relevant “money” takes months. So called “money” in the latter accounts is not normally classed as money.

5. Excess amounts of endo money cannot be a basic cause of inflation because the amount of such money is determined by the private sectors’s DESIRE for such money or by the private sector’s desire to do business. There may of course be an excess desire “to do business”, i.e. an outbreak of irrational exuberance, and that may cause excess inflation. But in that case the BASIC cause of the excess inflation is the irrational exuberance, not the amount of endo money.